The Towering Zeta Function

The Probabilistic Zeta Function

This paper is a summary of results on the PG(s) function, which is the reciprocal of the probabilistic zeta function for finite groups. This function gives the probability that s randomly chosen elements generate a group G, and information about the structure of the group G is embedded in it.

The Fibonacci Zeta Function

We consider the lacunary Dirichlet series obtained by taking the reciprocals of the s-th powers of the Fibonacci numbers. This series admits an analytic continuation to the entire complex plane. Its special values at integral arguments are then studied. If the argument is a negative integer, the value is algebraic. If the argument is a positive even integer, the value is transcendental by Neste...

Mollifying the Riemann Zeta-function

q-Riemann zeta function

We consider the modified q-analogue of Riemann zeta function which is defined by ζq(s)= ∑∞ n=1(qn(s−1)/[n]s), 0< q < 1, s ∈ C. In this paper, we give q-Bernoulli numbers which can be viewed as interpolation of the above q-analogue of Riemann zeta function at negative integers in the same way that Riemann zeta function interpolates Bernoulli numbers at negative integers. Also, we will treat some...

Towering tribute to botany

One of the world's greatest plant collections has won a top heritage award at a time when it is highlighting with a tree-top walkway the need to study the forest canopy which is one of the most crucial but least understood habitats.